Over the next six weeks, negotiators must strike a bipartisan compromise to slice more than $2 trillion from the federal budget by 2021, reduce the complex plan to writing and persuade a bitterly divided Congress to support it.

“I keep talking to other colleagues who have confidence that someone else is working things out,” said Sen. Chris Coons (D-Del.), a freshman member of the Budget Committee. “But I keep looking around thinking, ‘If we’re not doing it, then who is?’ ”

Even the broad goal of the talks is subject to dispute. Some lawmakers consider it too timid, arguing that the nation needs to find more than $4 trillion in savings by 2021 to avoid a debt crisis. Others view $2 trillion as impossibly ambitious. And hardly anybody wants to support the most critical part of the package: more borrowing authority for a nation already mired in red ink.

“There’s a large degree of apprehension,” said Sen. Bob Corker (R-Tenn.). “This is a seminal moment where we can do something great for the country. But there’s apprehension about it, because of the pace at which it’s going and the level of detail.”

With an Aug. 2 deadline nearing, along with the threat of turmoil in global financial markets if Congress doesn’t act, Vice President Biden is stepping up talks this week with six lawmakers from both parties in hopes of presenting a plan to President Obama and congressional leaders by July 4. So far, negotiators have identified many areas of consensus: Farmers are certain to lose some federal subsidies, for example. And federal workers will have to contribute more to finance their retirement.

But what Biden called “the philosophically big-ticket items” remain: the Republican demand for significant savings from Medicare, the biggest driver of future deficits, and the Democratic demand for fresh revenue.

“There are differences that are going to have to be bridged,” the vice president said last week, after emerging from a bargaining session at the Capitol. “We’re not going to cut any deal that can’t be sold.”

Still, leaders in both parties acknowledge that the sales job will not be easy, particularly in the House. Speaker John A. Boehner (R-Ohio) has demonstrated limited control over his independent-minded caucus, which is dominated by conservatives who are skeptical about the need to raise the legal limit on government borrowing.

For many, the memory is still fresh of that queasy day in September 2008 when Boehner struggled to get a third of his conference to support the Troubled Assets Relief Program bank bailout. The first vote failed, sending stock markets tumbling nearly 800 points.

Boehner and other GOP leaders say they are committed to raising the debt limit, now set at $14.3 trillion, to avoid default, an outcome they acknowledge could prove economically disastrous. Default could also prove politically disastrous: A new Washington Post-Pew Research Center poll found that more people say they would blame Republicans in Congress than Obama if debt-ceiling talks broke down.

Over the past two months, GOP leaders have been holding “listening sessions” to find out “where the center of gravity in our caucus is on this issue,” said House Budget Chairman Paul Ryan (Wis.), who is leading the sessions with Ways and Means Chairman Dave Camp (Mich.) and Majority Whip Kevin McCarthy (Calif.).

The requirement that any increase in the debt ceiling be matched dollar for dollar with spending cuts emerged from those sessions, Ryan said. But other sticky issues remain, with no clear path to resolution.

Although Republicans are demanding deep cuts in domestic programs, they are resisting sharp reductions at the Pentagon in the Biden talks, a key demand for many Democrats. Senior GOP aides said it would be hard to sell defense cuts to their skeptical troops.

“Guys like me, I’ll just say no,” said Rep. Duncan Hunter (R-Calif.), a veteran of Iraq and Afghanistan who argues that any reduction in military spending must be accompanied by a detailed analysis of the impact on national security. “Republicans, if they’re not careful, are going to saw off the third leg of the Republican stool. The leg of national security is going to get chopped off.”

Revenue is another major obstacle. Many Democrats say they could never vote to gut programs that help low- and middle-income families unless the wealthy are also forced to sacrifice. Democrats argue that Republicans should at least join them in eliminating corporate tax breaks that benefit major oil and gas companies and chief executives with private jets.

Senate Republicans have shown some openness to that approach, voting last week to eliminate tax breaks for ethanol blenders. But House leaders remain opposed to targeting credits and deductions without also overhauling the tax code and lowering rates. In the Biden talks, Republicans have so far declined to consider eliminating even certain temporary tax breaks, such as those for Puerto Rican rum and NASCAR tracks, that have been repeatedly lampooned by watchdog groups.

Coons, the Democrat from Delaware, is working on another point of conflict: the mechanism for enforcing a multi-year deal to cut spending. Republicans want annual spending limits, enforced by automatic spending cuts when the caps are breached. Obama wants a deficit limit that triggers both spending cuts and tax increases.

Coons is pressing a third approach, which would set annual targets for savings and trigger both tax increases and cuts to entitlement programs if the targets are not met.

“For me and my party, standing up and saying, ‘I’m willing to reduce entitlement benefits,’ is every bit as abhorrent as it is for Republicans to stand up and say, ‘We’re going to raise revenue,’ ” Coons said. If both priorities are at risk, he said, “that should be a strong enough motivator to keep us at the table, striving to meet these savings goals.”

Coons said several Republicans are interested in the idea, which was first proposed by the Bipartisan Policy Center, although none has endorsed it publicly. The idea has also won support from House Democratic leaders.

“I frankly don’t see a better alternative,” Coons said. “And I’m very worried that we’re running out of time.”